【正文】 xy y zyz xz yz zt x y zt x y zt x y z? ? ?? ? ?? ? ??? ? ??? ? ???? ? ??n n nn n nn n n? ? ? ? ? ?? ? ? ? ? ?? ? ? ? ? ?cos, cos, cos,cos, cos, cos,cos, cos, cos,x x yx zxy xy y zyz xz yzt x y zt x y zt x y z? ? ?? ? ?? ? ??? ? ??? ? ???? ? ??n n nn n nn n n? ? ? ? ? ?? ? ? ? ? ?? ? ? ? ? ?cos, cos, cos,cos, cos, cos,cos, cos, cos,x x yx zxy xy y zyz xz yz zt x y zt x y zt x y z? ? ?? ? ?? ? ??? ? ??? ? ???? ? ??n n nn n nn n n? ? ? ? ? ?? ? ? ? ? ?? ? ? ? ? ?cos, cos, cos,cos, cos, cos,cos, cos, cos,x x yx zxy xy y zyz xz yz zt x y zt x y zt x y z? ? ?? ? ?? ? ??? ? ??? ? ???? ? ??n n nn n nn n n? ? ? ? ? ?? ? ? ? ? ?? ? ? ? ? ?cos, cos, cos,cos, cos, cos,cos, cos, cos,x x yx zxy xy y zyz xz yz zt x y zt x y zt x y z? ? ?? ? ?? ? ??? ? ??? ? ???? ? ??n n nn n nn n n? ? ? ? ? ?? ? ? ? ? ?? ? ? ? ? ?cos, cos, cos,cos, cos, cos,cos, cos, cos,x x yx zxy xy y zyz xz yz zt x y zt x y zt x y z? ? ?? ? ?? ? ??? ? ??? ? ???? ? ??n n nn n nn n n S Depose S into Sx, Sy and Sz, then S2 = Sx2 + Sy2 + Sz2 These results clearly illustrate how the values for the normal and shear stress ponents of a force distributed over a plane inside of an object depends upon how you look at the point inside the object in the sense that the values of the shear and normal stresses at a point within a continuum depend upon the orientation of the plane you have chosen to view. σn = Sxl + Sym + Szn = σxl2 + σym2 + σzn2 + 2(τxylm + τyzmn + τzxnl) S n ? n ? n l = cos(n, x), m = cos(n, y) and n = cos(n,z) τn2 = S2 σn2 The above mentioned showes that if we know the 9 stresses ponents on the three mutually perpendicular planes as faces of a cube of infinitesimal size (element) which surround the given point we can determine the sterss ponents acting on any plane through the point. So these 9 stresses ponents can be used to represent the stress state of a point. x z y 一點應(yīng)力狀態(tài)可表示為： x?y?z?yz?xy?zx?167。?x39。?y39。x39。 39。?y39。 yxyyxx????????????yyxxyx???????????? ?????c oss i ns i nc os????????? ????c oss i ns i nc os?y?yx?xy?xxyxy ?x y39。 39。39。 of uniaxial stress: 單向應(yīng)力狀態(tài) The stress normal to the crosssectional surface: ? Stresses on oblique planes:（斜面上的應(yīng)力） Stresses: Forces: Now suppose we cut the prismatic bar at an angle θas shown below. How do the normal and shear ponents of stress acting on a plane at a given point change as we change the orientation of the plane at the point. 2. General Stress Systems in 2Dimensions （雙向應(yīng)力狀態(tài)） The stresses on the element ABCD in a ponent subjected to bined 2D loading (assuming no through thickness stresses, . plane stress) are schematically shown in the Figure. The reference system of coordinate axes are as shown also. What is the stress state on a chosen plane of interest? ? Consider rotating the element ABCD by an angle θ to the xaxis so that it now has axes of x’ and y’ orientated at angleθto the x and y axes. To determine the new stressesσx’,σy’ andτx’y’ on the element in terms of the original stresses consider the free body diagram of a prismatic element ADE and the stresses acting on it are as shown in the Figure. The normal stress σx’ and shear stress τx’y’ act on the plane AE and maintain the equilibrium of the prismatic element. The stresses σx’ andτx’y’ are obtained by resolution of forces in the respective directions. Transformation of Stresses（應(yīng)力變換） ????????? 39。 The state of stress at a point can normally be determined by puting the stresses acting on certain conveniently oriented planes passing through the point of interest. Stresses acting on any other planes can then be determined by means of simple, standardized analytical or graphical methods. If so we can use the stresses, acting on these conveniently oriented planes passing through the point, for representing the stress state of the given point, and that the stress state at this point is known. The selection of different cutting planes through a given point would, in general, result in stresses differing in both direction and magnitude. A plete description of the magnitudes and directions of stresses on all possible planes through the given point constitutes the state of stress at the given point. Problem: The stress ponents, on which of and how much different planes, can be used for representing the stress state of the given point? State of stress at a point（點的應(yīng)力狀態(tài)） 一點可以用無窮個微元表示，找出之間應(yīng)力的關(guān)系，稱為應(yīng)力狀態(tài)分析。 167。 ? 應(yīng)力 面 的概念：同一點處不同截面上的應(yīng)力不同。 c) Shear forces act parallel to the plane. Pairs of oppositely directed forces produce twisting effects called moments. 內(nèi)力 (1) 物體內(nèi)部分子或原子間的相互作用力 。 Force and stress Force（力） Structural mechanics describing the relations between external forces, internal forces(gravity, centrifugal, magic attractions, etc.) and deformation of structural materials. Forces are vector quantities, thus having direction and magnitude. They have special names depending upon their relationship to a reference plane: a) Compressive forces act normal and into the plane。彈性力學基本方程的建立為進一步的數(shù)值方法奠定了基礎(chǔ)。2022 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning? is a trademark used herein under license. Anisotropic behavior in a rolled aluminumlithium sheet material used in aerospace applications. The sketch relates the position of tensile bars to the mechanical properties that are obtained 彈性力學是固體力學的一個分支，研究彈性體由于外力作用或溫度改變等原因而發(fā)生的應(yīng)力、形變和位移。 使求解的方程 線性化 。 5. 小變形假定 假定位移和形變是微小的，即物體受力后物體內(nèi)各點位移遠遠小于物體原來的尺寸。 Linear Elasticity